Python Numpy数组初始化与核心操作指南
本文详解Python Numpy库中ndarray多维数组的初始化方法、核心属性及基本操作。涵盖从list/tuple转换、特殊值生成到均匀分布数组创建,深入解析元素级运算与矩阵乘法区别,并系统介绍多维数组的索引、切片及遍历技巧,助力高效数据处理。
Python作为一种高级、动态且支持多泛型的编程语言,其代码风格常接近伪代码,使得开发者能够以极少的行数实现强大功能,同时保持极高的可读性。
一.基础:
Numpy的核心数据类型为ndarray(多维数组),该对象具备以下关键属性:
ndarray.ndim:表示数组的维度数量; ndarray.shape:定义数组在每一维上的大小尺寸; ndarray.size:统计数组中所有元素的总数量; ndarray.dtype:标识数组内元素的数据类型(如numpy.int32、numpy.int16或numpy.float64等); ndarray.itemsize:指示每个元素所占用的字节数。
示例说明如下:
>>> import numpy as np
>>> a = np.arange(15).reshape(3, 5)
>>> a
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
>>> a.shape
(3, 5)
>>> a.ndim
2
>>> a.dtype.name
'int64'
>>> a.itemsize
8
>>> a.size
15
>>> type(a)
<type 'numpy.ndarray'>
>>> b = np.array([6, 7, 8])
>>> b
array([6, 7, 8])
>>> type(b)
<type 'numpy.ndarray'>
二.创建数组:
利用array函数可将tuple和list类型转换为array对象:
>>> import numpy as np
>>> a = np.array([2,3,4])
>>> a
array([2, 3, 4])
>>> a.dtype
dtype('int64')
>>> b = np.array([1.2, 3.5, 5.1])
>>> b.dtype
dtype('float64')
对于多维数组的构建:
>>> b = np.array([(1.5,2,3), (4,5,6)])
>>> b
array([[ 1.5, 2. , 3. ],
[ 4. , 5. , 6. ]])
在生成数组时指定特定数据类型:
>>> c = np.array( [ [1,2], [3,4] ], dtype=complex )
>>> c
array([[ 1.+0.j, 2.+0.j],
[ 3.+0.j, 4.+0.j]])
生成包含特殊值的数组:
ones:生成全1数组; zeros:生成全0数组; empty:生成随机数,具体数值取决于内存状态。
>>> np.zeros( (3,4) )
array([[ 0., 0., 0., 0.],
[ 0., 0., 0., 0.],
[ 0., 0., 0., 0.]])
>>> np.ones( (2,3,4), dtype=np.int16 ) # dtype can also be specified
array([[[ 1, 1, 1, 1],
[ 1, 1, 1, 1],
[ 1, 1, 1, 1]],
[[ 1, 1, 1, 1],
[ 1, 1, 1, 1],
[ 1, 1, 1, 1]]], dtype=int16)
>>> np.empty( (2,3) ) # uninitialized, output may vary
array([[ 3.73603959e-262, 6.02658058e-154, 6.55490914e-260],
[ 5.30498948e-313, 3.14673309e-307, 1.00000000e+000]])
生成均匀分布的array:
arange(参数为最小值、最大值、步长,区间左闭右开); linspace(参数为最小值、最大值、元素数量)。
>>> np.arange( 10, 30, 5 ) array([10, 15, 20, 25]) >>> np.arange( 0, 2, 0.3 ) # it accepts float arguments array([ 0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8]) >>> np.linspace( 0, 2, 9 ) # 9 numbers from 0 to 2 array([ 0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75, 2. ]) >>> x = np.linspace( 0, 2*pi, 100 ) # useful to evaluate function at lots of points
三.基本运算:
整个array按顺序参与运算:
>>> a = np.array( [20,30,40,50] ) >>> b = np.arange( 4 ) >>> b array([0, 1, 2, 3]) >>> c = a-b >>> c array([20, 29, 38, 47]) >>> b**2 array([0, 1, 4, 9]) >>> 10*np.sin(a) array([ 9.12945251, -9.88031624, 7.4511316 , -2.62374854]) >>> a<35 array([ True, True, False, False], dtype=bool)
两个二维数组使用*符号仍执行按位置一对一相乘,若需表示矩阵乘法,应使用dot函数:
>>> A = np.array( [[1,1],
... [0,1]] )
>>> B = np.array( [[2,0],
... [3,4]] )
>>> A*B # elementwise product
array([[2, 0],
[0, 4]])
>>> A.dot(B) # matrix product
array([[5, 4],
[3, 4]])
>>> np.dot(A, B) # another matrix product
array([[5, 4],
[3, 4]])
内置函数(min、max、sum)支持通过axis参数指定操作维度:
>>> b = np.arange(12).reshape(3,4)
>>> b
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>>
>>> b.sum(axis=0) # sum of each column
array([12, 15, 18, 21])
>>>
>>> b.min(axis=1) # min of each row
array([0, 4, 8])
>>>
>>> b.cumsum(axis=1) # cumulative sum along each row
array([[ 0, 1, 3, 6],
[ 4, 9, 15, 22],
[ 8, 17, 27, 38]])
Numpy同时提供大量全局函数:
>>> B = np.arange(3) >>> B array([0, 1, 2]) >>> np.exp(B) array([ 1. , 2.71828183, 7.3890561 ]) >>> np.sqrt(B) array([ 0. , 1. , 1.41421356]) >>> C = np.array([2., -1., 4.]) >>> np.add(B, C) array([ 2., 0., 6.])
四.寻址,索引和遍历:
一维数组的遍历语法与python list类似:
>>> a = np.arange(10)**3 >>> a array([ 0, 1, 8, 27, 64, 125, 216, 343, 512, 729]) >>> a[2] 8 >>> a[2:5] array([ 8, 27, 64]) >>> a[:6:2] = -1000 # equivalent to a[0:6:2] = -1000; from start to position 6, exclusive, set every 2nd element to -1000 >>> a array([-1000, 1, -1000, 27, -1000, 125, 216, 343, 512, 729]) >>> a[ : :-1] # reversed a array([ 729, 512, 343, 216, 125, -1000, 27, -1000, 1, -1000]) >>> for i in a: ... print(i**(1/3.)) ... nan 1.0 nan 3.0 nan 5.0 6.0 7.0 8.0 9.0
多维数组的访问需为每一维指定索引,顺序遵循先高维再低维的原则:
>>> def f(x,y):
... return 10*x+y
...
>>> b = np.fromfunction(f,(5,4),dtype=int)
>>> b
array([[ 0, 1, 2, 3],
[10, 11, 12, 13],
[20, 21, 22, 23],
[30, 31, 32, 33],
[40, 41, 42, 43]])
>>> b[2,3]
23
>>> b[0:5, 1] # each row in the second column of b
array([ 1, 11, 21, 31, 41])
>>> b[ : ,1] # equivalent to the previous example
array([ 1, 11, 21, 31, 41])
>>> b[1:3, : ] # each column in the second and third row of b
array([[10, 11, 12, 13],
[20, 21, 22, 23]])
When fewer indices are provided than the number of axes, the missing indices are considered complete slices:
>>>
>>> b[-1] # the last row. Equivalent to b[-1,:]
array([40, 41, 42, 43])
…符号表示将所有未指定索引的维度均赋为 :,:在python中表示该维所有元素:
>>> c = np.array( [[[ 0, 1, 2], # a 3D array (two stacked 2D arrays)
... [ 10, 12, 13]],
... [[100,101,102],
... [110,112,113]]])
>>> c.shape
(2, 2, 3)
>>> c[1,...] # same as c[1,:,:] or c[1]
array([[100, 101, 102],
[110, 112, 113]])
>>> c[...,2] # same as c[:,:,2]
array([[ 2, 13],
[102, 113]])
遍历:
如果只想遍历整个array可以直接使用:
>>> for row in b: ... print(row) ... [0 1 2 3] [10 11 12 13] [20 21 22 23] [30 31 32 33] [40 41 42 43]
但是如果要对每个元素进行操作,就要使用flat属性,这是一个遍历整个数组的迭代器
>>> for element in b.flat: ... print(element) ...
总结
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